1. Datums and Projections Demystifying the Reference Frame
Georgia Geospatial Conference 2012
Where We Are Now
Presentation by Lonnie Sears, LS
Originator ; Dave Doyle
NGS Chief Geodetic Surveyor

2. 1807 President Thomas Jefferson signs legislation establishing the Survey of the Coast

3. Our Positioning History
What’s In a Name?
Survey of the Coast
Coast Survey
US Coast and Geodetic Survey
National Geodetic Survey (NOS geodetic
functions)
National Ocean Service
National Geodetic Survey

4. ACRONYMS US R
NAD 27
GRS 80
ITRF 00
CORS
WGS 84
NAVD 88
NGVD 29
NAD 83

5. GLOBAL NAVIGATION SATELLITE SYSTEMS (GNSS)
POTENTIAL CONSTELLATION DEVELOPMENTS
(10 Years??)
GPS MODERNIZATION – BLOCK IIR-M & III
GLONASS ENHANCEMENTS
EUROPEAN UNION - GALILEO
CHINA - COMPASS
100+ Satellites
Second and Third Civil Frequency – GPS
More Robust Signal Transmissions
Real-Time Unaugmented 1 Meter (or better!) Accuracy

6. Orthometric Heights are related to the Geoid
GRACE Gravity Model 01
- Released July 2003
Orthometric Heights are
related to the Geoid
Image credit: University of Texas Center for Space Research and NASA

7. THE ELLIPSOID MATHEMATICAL MODEL OF THE EARTHN
Horizontal Coordinates and Ellipsoid Heights are related to the Ellipsoid b a
a = Semi major axis
b = Semi minor axis
f = a-b = Flattening a S

8. Earth - Lumpy Bumpy rock that is difficult if not impossible to describe with an equation.
Click
Let's take a sphere and put its center at the earth's center of mass
Then resize the sphere to best fit the earth - radius of 6, meters (later to become the semi-major axis)
This is a pretty good fit but we are out a little at the poles.
Now we can squash the sphere at the poles for a better fit. This creates an oblate spheroid.
Now the diameter along the polar (semi-minor) axis is 6,356,752 meters.
We can now describe the earth's shape with an equation.
a= meters
b= meters
f= 1/(a-b)/a =
We now have an ellipsoid - Since the Earth is in fact flattened slightly at the poles and bulges somewhat at the equator, the geometrical figure used in geodesy to most nearly approximate the shape of the Earth is an ellipsoid of revolution.
The ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. An ellipsoid of revolution describing the figure of the Earth is called a reference ellipsoid.
Definition:
NAD83 – The North American Datum of 1983 – the earth centered, earth fixed reference system that uses the GRS80 ellipsoid
An ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. An ellipsoid of revolution describing the figure of the Earth is called a reference ellipsoid.
Earth
The rotation of the Earth creates the equatorial bulge so that the equatorial diameter is 43 km larger than the pole to pole diameter.[37] The largest local deviations in the rocky surface of the Earth are Mount Everest (8,848 m above local sea level) and the Mariana Trench (10,911 m below local sea level). Hence compared to a perfect ellipsoid, the Earth has a tolerance of about one part in about 584, or 0.17%, which is less than the 0.22% tolerance allowed in billiard balls.[38] Because of the bulge, the feature farthest from the center of the Earth is actually Mount Chimborazo in Ecuador.[39]
GRS80
NAD83
b = 6,356, m
This shape is what we reference NAD83 and the GPS system to.
Both the horizontal and vertical coordinates originate with this surface.
The Pythagorean concept of a spherical Earth offers a simple surface which is mathematically easy to deal with. Many astronomical and navigational computations use it as a surface representing the Earth. While the sphere is a close approximation of the true figure of the Earth and satisfactory for many purposes, to the geodesists interested in the measurement of long distances—spanning continents and oceans—a more exact figure is necessary. Closer approximations range from modelling the shape of the entire Earth as an oblate spheroid or an oblate ellipsoid to the use of spherical harmonics or local approximations in terms of local reference ellipsoids. The idea of a planar or flat surface for Earth, however, is still acceptable for surveys of small areas as local topography is more important than the curvature. Plane-table surveys are made for relatively small areas and no account is taken of the curvature of the Earth. A survey of a city would likely be computed as though the Earth were a plane surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size and shape of the total Earth.
a= meters
b= meters
f= 1/((a-b)/a) =
Squash the sphere to fit at the poles
a = 6,378, m

9. ELLIPSOID - GEOID RELATIONSHIP
H = Orthometric Height (NAVD 88)
h = Ellipsoidal Height [NAD 83 (2007) or (CORS96)]
N = Geoid Height (GEOID 09)
H = h – [N] h H N
GEOID09
Geoid
Ellipsoid
GRS80 9

10. National Spatial Reference System (NSRS)
Consistent National Coordinate System
Latitude
Longitude
Height
Scale
Gravity
Orientation
and how these values change with time

11. NATIONAL SPATIAL REFERENCE SYSTEM
ACCURATE -- cm accuracy on a global scale
MULTIPURPOSE -- Supports Geodesy, Geophysics, Land Surveying, Navigation, Mapping, Charting and GIS activities
ACTIVE -- Accessible through Continuously Operating Reference Stations (CORS) and derived products
INTEGRATED -- Related to International services and standards (e.g. International Earth Rotation and Reference Systems Service, International GNSS Service etc.)

12. Networks of geodetic control points
NSRS COMPONENTS
National Shoreline
- Consistent, accurate, and up-to-date
Networks of geodetic control points
- Permanently marked passive survey monuments
a consistent, accurate, up-to-date National Shoreline;
.the National CORS, a set of Global Positioning System (GPS) Continuously Operating Reference Stations meeting NOAA geodetic standards for installation, operation, and data distribution;
.a network of permanently marked geodetic control points; and
.a set of accurate models describing dynamic geophysical processes affecting spatial measurements.
National CORS Network
- A network of GPS Continuously Operating Reference Stations
Tools
Models of geophysical effects on spatial measurements
e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD
Tools
Models of geophysical effects on spatial measurements
e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD

13. GEODETIC DATUMS
A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth. Specific geodetic datums are usually given distinctive names. (e.g., North American Datum of 1983, European Datum 1950, National Geodetic Vertical Datum of 1929)
Characterized by:
A set of physical monuments, related by survey measurements and resulting coordinates (horizontal and/or vertical) for those monuments

14. GEODETIC DATUMS HORIZONTAL VERTICAL/GEOPOTENTIAL GEOMETRIC
2-D (Latitude and Longitude) (e.g. NAD 27, NAD 83 (1986))
VERTICAL/GEOPOTENTIAL
1-D (Orthometric Height) (e.g. NGVD 29, NAVD 88, Local Tidal)
GEOMETRIC
3-D (Latitude, Longitude and Ellipsoid Height)
Fixed and Stable(?) - Coordinates seldom change
(e.g. NAD 83 (1993), NAD 83 (2007))
also
4-D (Latitude, Longitude, Ellipsoid Height, Velocities) Coordinates change with time
(e.g. ITRF00, ITRF05)

15. HORIZONTAL DATUMS 8 Constants
3 – specify the location of the origin of the coordinate system.
3– specify the orientation of the coordinate system.
2 – specify the dimensions of the reference ellipsoid

16. VERTICAL DATUMS Datum Types
A set of fundamental elevations to which other elevations are referred.
Datum Types
Tidal – Defined by observation of tidal variations over some period of time
(MSL, MLLW, MLW, MHW, MHHW etc.)
(NOS Center for Operational Oceanographic Products and Services)
(CO-OPS)
Geodetic – Tided to Local Mean Sea Level at one or more points at some epoch
(NAVD 88, IGLD85)

17. HISTORICAL VERTICAL DATUMS OF THE UNITED STATES
First General Adjustment
Second General Adjustment
Third General Adjustment
Fourth General Adjustment
Sea Level Datum of 1929
National Geodetic Vertical Datum of 1929
(NGVD 29)
Guam 1963

18. NGVD29
The National Geodetic Vertical Datum of 1929 is referenced to 26 tide gauges in the US and Canada

19. NAVD88
The North American Vertical Datum of 1988 is referenced to a single tide gauge in Canada

20. VERTICAL DATUMS OF THE UNITED STATES Current Reference Systems
North American Vertical Datum of 1988
(NAVD 88)
Federal Register Notice: Vol. 58, No. 120, June 24, 1993, pg
“Affirmation of Vertical Datum for Surveying and Mapping Activities”
American Samoa Vertical Datum of 2002
(ASVD 02)
Northern Marians Vertical Datum of 2003
(NMVD 03)
Guam Vertical Datum of 2004
(GUVD 04)
Federal Register Notices for American Samoa, Guam and Northern Marians: Vol. 74, No. 13, January 22, 2009, pgs

21. VERTICAL DATUMS OF THE UNITED STATES Works in Progress
Puerto Rico Vertical Datum of 2002 (PRVD 02)
Virgin Island Vertical Datum of 2009 (VIVD 09)
Hawaiian Islands Vertical Datum
(HIVD)

22. HISTORICAL HORIZONTAL DATUMS OF THE UNITED STATES
Bessel Ellipsoid
Camp Colonna Datum
St. Paul Island Datum
New England Datum
Flaxman Island Datum
UnAlaska Datum
U.S. Standard Datum
Golofnin Bay Datum
Valdez Datum
North American Datum
Kripniyuk Datum
Yakutat Datum
North American Datum of 1927
Point Barrow Datum
Yukon Datum
Johnson Island 1961
Puerto Rico Datum
Port Clarence Datum
Midway Astro 1961
Old Hawaiian Datum
SE Alaska Datum
American Samoa Datum 1962
St. George Island Datum
Wake Island Astro 1952
Guam Datum 1963
St. Lawrence Island Datum
Barter Island Datum
St. Michael Datum

23. NORTH AMERICAN DATUM OF 1983
Federal Register Notice: Vol. 54, No. 113, June 14, 1989, pg
“Affirmation of Datum for Surveying and Mapping Activities”
NAD 83 (1986) – 2D & passive ~ 1m national integrity
(1986 – 1990)
NAD 83 (199x) – 3D & passive ~ 10 cm national integrity
(1990 – 1997)
NAD 83 (CORS96) – 4D & active ~ 2 cm national integrity
(1994 – Present)
NAD 83 (2007) – 3D & passive ~ 2 cm relative to CORS
(2007 – Present)

24. Tectonic Motions

25. International Earth Rotation and Reference System Service (IERS) (http://www.iers.org)
The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modeling required to define origin, scale, orientation and time evolution
ITRS is realized by the International Terrestrial Reference Frame (ITRF) based upon estimated coordinates and velocities of a set of stations observed by Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging ( SLR), Global Positioning System and GLONASS (GNSS), and Doppler Orbitography and Radio- positioning Integrated by Satellite ( DORIS).
ITRF89, ITRF90, ITRF91, ITRF92, ITRF93, ITRF94, ITRF95, ITRF96, ITRF97, ITRF2000, ITRF2005, ITRF2008, ITRF2010

26. International Terrestrial Reference Frame
4 Global Independent Positioning Technologies
International Global Navigation Satellite Systems Service (IGS)
International Laser Ranging Service (ILRS)
International Very Long Baseline Service (IVS)
International DORIS Service (IDS)

27. If requirements are greater than 3m then Yes
ARE NAD 83 & WGS 84 THE SAME?
IT DEPENDS
If requirements are greater than 3m then Yes
If requirements are less than 3m then No
Federal Register Notice: Vol. 60, No. 157, August 15, 1995, pg
“Use of NAD 83/WGS 84 Datum Tag on Mapping Products”

28. HOW MANY WGS 84s HAVE THERE BEEN????
WORLD GEODETIC SYSTEM 1984
DATUM = WGS 84(G1150)
Datum redefined with respect to the International
Terrestrial Reference Frame of 2000 (ITRF00)
+/- 2 cm in each component
(Proceedings of the ION GPS-02)
DATUM = WGS 84(G873)
Datum redefined with respect to the International Terrestrial Reference Frame of 1994 (ITRF94)
+/- 10 cm in each component
(Proceedings of the ION GPS-97 pgs )
DATUM = WGS 84
RELEASED - SEPTEMBER 1987
BASED ON OBSERVATIONS AT MORE THAN 1900 DOPPLER STATIONS
HOW MANY WGS 84s
HAVE THERE BEEN????
DATUM = WGS 84(G730)
Datum redefined with respect to the International Terrestrial Reference Frame of 1992 (ITRF92)
+/- 20 cm in each component
(Proceedings of the ION GPS-94 pgs )

29. ARE NAD 83 & WGS 84 THE SAME?
NAD 83 to ITRF00
dX = m
dY = m
dZ = m
S = 0.62 x 10-9
rX = mas
rY = mas
rZ = mas

30. MY SOFTWARE SAYS I’M WORKING IN WGS-84
Unless you are doing autonomous positioning
(point positioning +/ meters)
you’re probably NOT in WGS-84
Project tied to WGS-84 control points obtained
from the Defense Department -- Good Luck!
You’re really working in the same reference frame
as your control points -- NAD 83?

31. PLANE COORDINATE SYSTEMS
STATE PLANE AND UNIVERSAL TRANSVERSE MERCATOR GRID COORDINATES ARE A DIRECT MATHEMATICAL CONVERSION FROM LATITUDE AND LONGITUDE TO A CARTESIAN NORTHING AND EASTING (Y & X) COORDINATE SYSTEM, AND MUST MAINTAIN THE SAME DATUM TAG [e.g. NAD 27 or NAD 83] AS THE LATITUDE AND LONGITUDE)

32. So What Is A Projection
NORTHING
EASTING

33. MAP PROJECTIONS CONIC AND CLYNRIDCAL

34. UTM ZONES

36. STATE PLANE COORDINATE ZONES

37. What Are State Plane Coordinates
State plane coordinates are the projection of latitudes and longitudes from the GRS80 ellipsoid
To:
A flat mapping surface that is usually defined by state law

38. STATE PLANE COORDINATE SYSTEM 1927
Developed by U.S. Coast and Geodetic Survey from a request in 1933 from the North Carolina Department of Transportation
Two basic map projections used:
Lambert Conformal Conic – States or parts of states that have a more East-West orientation
Transverse Mercator – States or parts of states that have a more North-South orientation
Zone boundaries along International, State and county boundaries
Zones typically 154 miles wide – this limits the maximum geodetic to grid distance distortion to 1:10,000
All coordinate values in U.S. Survey Feet
Conversions to/from latitude & longitude calculated using tables
(e.g. USC&GS Special Publication. 316 Plane Coordinate Projections Tables – New Jersey)
State Plane Coordinates by Automatic Data Processing (USC&GS 62-4)

39. STATE PLANE COORDINATE SYSTEM 1983
Geometric parameters of original SPC zones left unchanged unless requested by “the State”
All states get new false northing and false easting defined in meters.
All values in meters – conversions to feet defined by individual state legislation or Federal Register Notice
1 m = U.S. Survey Feet
1 m = International Feet

40. Utah is now a U.S. Survey Foot State
(Blue)

41. PLANE COORDINATE CONVERSION TOOLS
UTM
UTMS (Both NAD 27 & NAD 83)
CORPSCON (Both NAD 27 & NAD 83)
STATE PLANE COORDINATES
GPPCGP (NAD 27 only)
SPCS83 (NAD 83 only)

42. DATUM TRANSFORMATIONS
1. WHAT DATUM ARE THE EXISTING COORDINATES/HEIGHTS ON?
2. WHAT DATUM DO I WANT THE NEW COORDINATES/HEIGHTS ON?
3. HOW LARGE A GEOGRAPHICAL AREA DO I WANT TO CONVERT AT ONE TIME?
4. HOW MANY POINTS ARE COMMON TO BOTH DATUMS?
5. WHAT IS THE DISTRIBUTION OF THE COMMON POINTS?
6. HOW ACCURATE ARE THE EXISTING COORDINATES/HEIGHTS?
0.01 Meter
0.1 Meter
1.0 Meter
7. HOW ACCURATE DO I WANT THE NEW COORDINATES/HEIGHTS?

43. DATUM TRANSFORMATION IDEAL METHOD
SATISFIES ALL USERS’ REQUIREMENTS
CAPABLE OF TRANSFORMING LARGE DATASETS
NEAR-REAL TIME APPLICATIONS
SIMPLE - METHOD SHOULD NOT REQUIRE AN EXPERT OR DECISIONS TO BE MADE
ACCURATE

44. DATUM TRANSFORMATIONS
MOLODENSKY
For continental regions accuracy can be +/- 8 to 10 meters
Does not model network distortions very well.
Assumes heights in both systems are ellipsoidal (NAD 27 did not have ellipsoidal heights).

45. NGS DATUM TRANSFORMATION MODELS
VERTCON
(NGVD 29 only)
NADCON
(NAD 27, OLD HAWAIIAN, PUERTO RICO, 3 ALASKA ISLANDS)
(HPGN/HARN)
Federal Register Notice: Vol. 72, No. 132, July 11, 2007, pg
“Notice to Adopt a Standard Model fro Mathematical Vertical Datum Transformations”
Federal Register Notice: Vol. 55, No. 155, August 10, 1990, pg
“Notice to Adopt Standard Method for Mathematical Horizontal Datum Transformation”

46. DATUM TRANSFORMATIONS
MOLODENSKY
Converts latitude, longitude and ellipsoidal height to X,Y,Z Earth-Centered Coordinates.
Applies a 3-dimensional change in the origin (dX, dY,dZ)
Applies a change in the size and shape of the reference ellipsoid
Converts new X,Y,Z Earth-Centered Coordinates back to latitude, longitude and ellipsoidal height

47. MOLODENSKY TRANSFORMATION

48. NADCON d = +0.12344 dλ = -1.87842 d = +0.12249 dλ = -1.88963
 =
λ =
d =
dλ =
d =
dλ =
d =
dλ =
d =
dλ =
d =
dλ =
d =
dλ =

49. COORDINATE COMPARISON NAD 27 to NAD 83(1993)
MOLODENSKY
ADJUSTED vs. TRANSFORMED
Station: OBSERVATORY (HV7843)
LATITUDE LONGITUDE
PUBLISHED
MOLODENSKY
.20828” ”
6.422 m m
THIS CORRESPONDS TO A POSITIONAL
DIFFERENCE OF m (21.08 ft)

50. COORDINATE COMPARISON NAD 27 to NAD 83(1993)
NADCON
ADJUSTED vs. TRANSFORMED
Station: OBSERVATORY (HV7843)
LATITUDE LONGITUDE
PUBLISHED
NADCON
.00052” ”
0.016 m m
THIS CORRESPONDS TO A POSITIONAL
DIFFERENCE OF m (0.20 ft)

51. GOOD COORDINATION BEGINS WITH
GOOD COORDINATES
GEOGRAPHY WITHOUT GEODESY IS A FELONY